Question

Differential equations question.

dp/dt = 0.3 (1-p/10) (p/10-2)p

1. (5 points) Consider the given population model, where P(t) is the population at time t A. For what values of P is the population in equilibrium? B. For what values of P is it increasing? C. For what values is it decreasing? : (i-T-YE -2) p dt120 her

Answer 1

dp/dt = 0.3 (1-p/10) (p/10-2)p

for equilibrium, dp/dt=0

  0.3 (1-p/10) (p/10-2)p=0

p=10 or p=20 or p=0

for increasing p , dp/dt>0

  0.3 (1-p/10) (p/10-2)p>0

10<p<20

for decreasing p , dp/dt<0

  0.3 (1-p/10) (p/10-2)p<0

0<p<10 or p>20